It's like this-
As for every integer $n>5,10\mid n!$ so the last digit (suppose $a$) will be-
$a\equiv 1!+2!+3!+4!\equiv 1+2+6+4(mod 10)$
$a\equiv 3(mod 10)$
Or,$a=3$(as $a<10$)
Search found 1175 matches
- Fri Feb 04, 2011 12:55 pm
- Forum: Secondary: Solved
- Topic: Dhaka Secondary 2009/6
- Replies: 7
- Views: 6504
- Thu Feb 03, 2011 9:07 pm
- Forum: Secondary: Solved
- Topic: Rangpur Secondary 2011/6
- Replies: 7
- Views: 5509
Re: Rangpur Secondary 2011/6
Here,$N$ must be equal to $15x$ where $x\neq7y$.Then $15$ is the answer.
- Thu Feb 03, 2011 9:01 pm
- Forum: Secondary: Solved
- Topic: Rangpur Secondary 2011/5
- Replies: 3
- Views: 4169
Re: Rangpur Secondary 2011/5
Stewert's theorem on triangle $ABC$- $PR(OS^2+OR\times OP)=PS^2\times OR+SR^2\times OP$ $\Rightarrow PR(6^2+OR\times OP)=12^2\times OR+12^2OP$ $\Rightarrow PR(6^2+OR\times OP)=12^2(OR+OP)=12^2\times PR$ $\Rightarrow 6^2+OR\times OP=12^2$ $\Rightarrow OR\times OP=144-36=108$ $\Rightarrow OS\times OQ=...
- Thu Feb 03, 2011 8:30 pm
- Forum: Secondary: Solved
- Topic: Rangpur Secondary 2011/4
- Replies: 4
- Views: 4397
Re: Rangpur Secondary 2011/4
It's really easy , just triangle inequality $a+b>c$ does the trick........
- Thu Feb 03, 2011 8:25 pm
- Forum: Secondary: Solved
- Topic: Rangpur Secondary 2011/3
- Replies: 6
- Views: 13838
Re: Rangpur Secondary 2011/3
Tahmid-please write $2^{11}$ as 2^{11} in latex,because if you write 2^11 in latex it will be$2^11$Tahmid Hasan wrote:$$2048=2^11=2^62^5=64*32$$
so the difference is 32.
- Thu Feb 03, 2011 8:20 pm
- Forum: Secondary: Solved
- Topic: Rangpur Secondary 2011/1
- Replies: 4
- Views: 9184
Re: Rangpur Secondary 2011/1
Yup....it is $9^3=729$
- Thu Feb 03, 2011 6:13 pm
- Forum: Secondary: Solved
- Topic: Rangpur Secondary 2011/7
- Replies: 3
- Views: 3604
Re: Rangpur Secondary 2011/7
Just another way-
$f(x+0)=x+f(0)$
So,$f(x)=x+19$
Which means $f(1952)=1952+19=1971$
$f(x+0)=x+f(0)$
So,$f(x)=x+19$
Which means $f(1952)=1952+19=1971$
- Thu Feb 03, 2011 9:23 am
- Forum: H. Secondary: Solved
- Topic: Rangpur Higher Secondary 2011/4
- Replies: 2
- Views: 7578
Re: Rangpur Higher Secondary 2011/4
The answer is -
- Tue Feb 01, 2011 9:43 am
- Forum: Secondary: Solved
- Topic: Dhaka Secondary 2011/7
- Replies: 11
- Views: 17723
Re: Dhaka Secondary 2011/7
There are many people who try the problem themselves,without knowing the solution.My solution is only to ensure they get the real answer ,and so I have to hide the solution. The answer is NOT 6. The word "repetition" changes everything.It means that the name "aaa" or "bbb" is allowed. So as $5^3=125...
- Sun Jan 30, 2011 9:41 am
- Forum: Secondary: Solved
- Topic: Dhaka Secondary 2011/1 (Higher Secondary 2011/1)
- Replies: 9
- Views: 14615
Re: Dhaka Secondary 2011/1 (Higher Secondary 2011/1)
The answer isn't the one Tahmid posted,it is as follows- The answer is 76. Here we must know that in the silver ring set,there are 12 kinds,and in the gold ring set,there are 10 kinds.So at least 2 kinds of silver ring is different from the gold kinds.Now if we pick up 75 rings , all of them can be...